TY - JOUR
T1 - Ramified covers of abelian varieties over torsion fields
AU - Bary-Soroker, Lior
AU - Fehm, Arno
AU - Petersen, Sebastian
N1 - Publisher Copyright:
© 2023 Walter de Gruyter GmbH, Berlin/Boston.
PY - 2023/12/1
Y1 - 2023/12/1
N2 - We study rational points on ramified covers of abelian varieties over certain infinite Galois extensions of ℚ. In particular, we prove that every elliptic curve E over ℚ has the weak Hilbert property of Corvaja and Zannier both over the maximal abelian extension ℚab of ℚ, and over the field ℚ (A tor) obtained by adjoining to ℚ all torsion points of some abelian variety A over ℚ.
AB - We study rational points on ramified covers of abelian varieties over certain infinite Galois extensions of ℚ. In particular, we prove that every elliptic curve E over ℚ has the weak Hilbert property of Corvaja and Zannier both over the maximal abelian extension ℚab of ℚ, and over the field ℚ (A tor) obtained by adjoining to ℚ all torsion points of some abelian variety A over ℚ.
UR - http://www.scopus.com/inward/record.url?scp=85175693194&partnerID=8YFLogxK
U2 - 10.1515/crelle-2023-0077
DO - 10.1515/crelle-2023-0077
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AN - SCOPUS:85175693194
SN - 0075-4102
VL - 2023
SP - 185
EP - 211
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
IS - 805
ER -